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How is K_w defined, and what is its numerical value at 25 °C?
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14. Acids and Bases
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객관식
Calculate the Kw of pure water given the pH = 6.34.
A
4.57 × 10−7
B
6.76 × 10−4
C
2.09 × 10−13
D
4.57 × 10−14
검증된 단계별 안내1
Recall that pH is defined as the negative logarithm (base 10) of the hydrogen ion concentration: \(\mathrm{pH} = -\log_{10}[\mathrm{H}^+]\). Use this to find the concentration of hydrogen ions, \([\mathrm{H}^+]\), by rearranging the formula: \([\mathrm{H}^+] = 10^{-\mathrm{pH}}\).
Calculate \([\mathrm{H}^+]\) using the given pH value of 6.34 by substituting it into the equation from step 1.
In pure water, the concentration of hydrogen ions \([\mathrm{H}^+]\) is equal to the concentration of hydroxide ions \([\mathrm{OH}^-]\) because water self-ionizes into equal amounts of \(\mathrm{H}^+\) and \(\mathrm{OH}^-\) ions.
Use the ion product constant of water, \(K_w\), which is defined as \(K_w = [\mathrm{H}^+][\mathrm{OH}^-]\). Since \([\mathrm{H}^+] = [\mathrm{OH}^-]\), rewrite this as \(K_w = [\mathrm{H}^+]^2\).
Finally, calculate \(K_w\) by squaring the hydrogen ion concentration found in step 2: \(K_w = ([\mathrm{H}^+])^2\).
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